Z-prime gamma submodule of gamma modules

Let $R$ be a $Gamma$-ring and $partial$ be an $RGamma$-module. A proper $RGamma$-submodule. $T$ of an $RGamma$-module $partial$ is called Z-prime $RGamma$-submodule if for each $tin partial, gamma in Gamma$ and $f in partial^{ast}=Hom_{R_{Gamma}}(partial,R),f(t)gamma t in T$ implies that either $t in T$ or $f(t)in [T: _{R_{Gamma}} partial]$. The purpose of this paper is to introduce interesting theorems and properties of Z- prime $RGamma$-submodule of $RGamma$-module and the relation of Z-prime $RGamma$-submodule, which represents of generalization Z-prime R-submodule of R-module.